论文标题
量化量子设备的高维度
Quantifying the high-dimensionality of quantum devices
论文作者
论文摘要
我们引入了高维量子设备的平均维度（或连贯性）的度量。这包括一组量子测量，转向组合和量子通道。对于测量和通道，我们的度量对应于平均压缩维度，而对于量子转向，我们获得了平均纠缠维度（称为Schmidt度量）的半设备独立量化器。我们在所有三种情况下分析了该度量。首先，我们证明可以通过半定准则和低维系统中的频道和测量结果确定它。其次，我们认为由此产生的转向措施是对众所周知的转向重量的高维概括。最后，我们分析了渐近环境中度量的行为。更确切地说，我们表明，两分量子状态的渐近施密特度量等于纠缠成本，并显示最近引入的转向组合形成纠缠如何与我们的渐近案例中的措施有关。
We introduce a measure of average dimensionality (or coherence) for high-dimensional quantum devices. This includes sets of quantum measurements, steering assemblages, and quantum channels. For measurements and channels, our measure corresponds to an average compression dimension, whereas for quantum steering we get a semi-device independent quantifier for the average entanglement dimensionality known as the Schmidt measure. We analyse the measure in all three scenarios. First, we show that it can be decided via semi-definite programming for channels and measurements in low-dimensional systems. Second, we argue that the resulting steering measure is a high-dimensional generalisation of the well-known steering weight. Finally, we analyse the behaviour of the measure in the asymptotic setting. More precisely, we show that the asymptotic Schmidt measure of bipartite quantum states is equal to the entanglement cost and show how the recently introduced entanglement of formation for steering assemblages can be related to our measure in the asymptotic case.
